It’s relatively simple to change your name on Facebook. The site recommends you first review their name standards; this is pretty standard, as you want to make sure the change will be accepted. Once you’ve done that, you go to your settings tab. From there, you find the tab entitled “Name” and that’s where you can change your name. After you enter the new name, you review changes, and then save the changes by entering your passwords.
As a side note, the kinds of names that aren’t allowed are few. Symbols and numbers aren’t usually allowed. Religious or professional titles aren’t allowed; this is a public social site, after all. Offensive language isn’t allowed in your name, either. If you abide by all the rules, and your name isn’t changing on the site, there is a help page for that.